**Introduction of Lines And Angles** Notes

**Parallel lines with a transversal**

- ∠1=∠5,∠2=∠6,∠4=∠8 and ∠3=∠7(Corresponding angles)
- ∠3=∠5,∠4=∠6 (Alternate interior angles)
- ∠1=∠7,∠2=∠8 (Alternate exterior angles)

**Lines parallel to the same line**

Lines that are parallel to the same line are also parallel to each other.

**Introduction to Geometry**

### Angles and types of angles

When 2 rays originate from the same point at different directions, they form an angle.

– The rays are called arms and the common point is called the vertex

– Types of angles : (i) Acute angle 0∘<a<90∘

(ii) Right angle a=90∘

(iii) Obtuse angle : 90∘<a<180∘

(iv) Straight angle =180∘

(v) Reflex Angle 180∘<a<360∘

(vi) Angles that add up to 90∘ are complementary angles

(vii) Angles that add up to 180∘ are called supplementary angles.

**Intersecting Lines and Associated Angles**

**Intersecting and Non-Intersecting lines**

- When 2 lines meet at a point they are called intersecting
- When 2 lines never meet at a point, they are called non-intersecting or parallel lines

Adjacent angles

2 angles are adjacent if they have the same vertex and one common point.

**Linear Pair**

When 2 adjacent angles are supplementary, i.e they form a straight line (add up to 180∘), they are called a linear pair.

**Vertically opposite angles**

When two lines intersect at a point, they form equal angles that are vertically opposite to each other.

**Basic Properties of a Triangle**

**Triangle and sum of its internal angles**

Sum of all angles of a triangle add up to 180∘

**An exterior angle of a triangle = sum of opposite internal angles**

– If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles

– ∠4=∠1+∠2